The assignment of numerical value to objects' physical properties
Dimension
Relates the size of a magnitude of property to a numerical suit (mer) of measurement
Fundamental Quantities
Basic quantities that are independent from one another
FIQ Units
Units corresponding to fundamental quantities, called base units
Derived Quantities
Quantities resulting from combinations of any of the fundamentalquantities
Unit conversion examples using meters
The value of different fundamental and derived quantities is sometimes composed of very large or small numbers
When we want to quantify or numerically describe the property of an event, a property of an object or characteristics of an object, we can do it by counting or by using instruments to measure
Measurement
The process of assignment of numerical value to an object's physical properties
Physical quantity
Any number that describes a physical property, consisting of a number and corresponding units
Seven fundamental quantities
Length
Mass
Time
Temperature
Electric current
Luminous intensity
Amount of substance
Fundamental units/Base units
Units that can only be defined by the way they were measured, not derived from other units
Derived units/Derived quantities
Units defined by describing how they were calculated from other quantities, whether fundamental or derived
The two most widely used systems of measurement are the metric system (SI units) and the English system (FPS system)
Most countries around the world use the metric system as the basis for their standard unit of measurement
The metric system is easier to convert between units as the conversion factors are multiples of 10, unlike the irregular conversion factors in the English system
Using the same unit of measurement is important for accuracy and reproducibility of experimental results
Dimensional analysis
The process of using units to convert from one unit to another
Larger physical quantity units of the same physical quantities for English systems unlike metric systems where you just need to recall that you need to multiply it by 10 raised to a certain degree so multiples of 10
The main reason why most countries change from using English system to metric systems is to secure accuracy and reproducibility or precision in the result of our measurements and experiments
Dimensional analysis
1. Identify the value to be converted
2. Find the conversion factor
3. Multiply the original value by the conversion factor
4. Write the equivalent value
Conversion factor
Numerical fraction or ratio between quantities which can be used as a multiplication factor for converting one unit to another
Common conversion factors
Length
Mass
Time
Speed
Force
Other derived and fundamental quantities
Prefixes
Used to describe the exponential factor in unit conversion
Metric system has conversion factors in multiples of 10, unlike irregular English system
Can convert between metric units and English units using conversion factors
Sometimes only part of the unit needs to be converted, e.g. converting 10 miles per hour to km/h
To convert 10 miles/h to km/h, only need to convert miles to km using conversion factor of 1 mile = 1.609 km
10 miles/h = 16.09 km/h (rounded to 2 sig figs)
don't need to convert but litto we need to convert miles to kilometers so there are problems where in the bythology only part of the of the whole unit so in this um type of situation so modeling them so i just identify again your conversion factor needed
Conversion factor
The ratio that allows you to convert one unit to another
In one mile there are 1.609 kilometers
Converting miles to kilometers
Multiply miles by 1.609 to get kilometers
10 miles per hour is equal to 16.09 kilometers per hour
To express the result in the correct number of significant figures, you need to round it off
Converting kilometers per hour to meters per second
1. Write the original value with unit
2. Convert kilometers to meters (1 km = 1000 m)
3. Convert hours to seconds (1 hr = 3600 s)
4. Perform the calculation
55 kilometers per hour is equal to 15 meters per second
Converting yards per second to meters per second
1. Write the original value with unit
2. Convert yards to meters (1 yard = 0.9144 m)
3. Perform the calculation
Converting meters to feet
1. Write the original value with unit
2. Convert meters to feet (1 m = 3.281 ft)
3. Perform the calculation
Dimensional analysis is the process of using units and dimensions to solve problems